Worksheet: Centering in Cubic Lattices

In this worksheet, we will practice describing the atomic coordinates, packing densities, and hole geometries in cubic lattices.

Q1:

What is the coordination number of a cobalt atom in the hexagonal close-packed structure of cobalt metal?

Q2:

What is the coordination number of a chromium atom in the body-centered cubic structure of chromium metal?

Q3:

A unit cell contains equivalent atoms at (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), (1,1,1), and 12,12,12. Which letter denotes the type of centering displayed by this unit cell?

  • AP
  • BI
  • CC
  • DF
  • ER

Q4:

The compound MX contains a metal ion M with an ionic radius 49% smaller than that of the anion X. Determine which of the following statements is false, given that the metal ions M have the following coordinates: (0,0,0),(0,1,0),(0,0,1),(0,1,1),(1,0,0),(1,1,0),(1,0,1),(1,1,1),12,12,0,12,0,12,0,12,12,12,12,1,12,1,12,1,12,12.

  • AThe metal ions are hexacoordinate.
  • BThe lattice has a body-centered structure.
  • CThe lattice adopts the cubic structure with the highest packing efficiency.
  • DThere are four M ions within the unit cell.

Q5:

For a face-centered cubic crystal system MX, the metal M is located at the coordinates (1/2, 1/2, 1/2). What would you expect the metal’s coordination number to be?

Q6:

Cesium and sodium are group 1 metals, but the coordination number of cesium in the CsCl unit cell is 8, whereas the coordination number of sodium in the NaCl unit cell is 6. What allows cesium to have a larger coordination number?

  • AChlorine is too electronegative to be completely compatible with sodium.
  • BThe NaCl radius ratio is greater than that of CsCl, forcing anions farther from the metal cation.
  • CSodium has a larger ionic radius than cesium, allowing for less anion attraction.
  • DDue to its size, cesium makes more contact with adjacent anions than sodium does.

Q7:

Fill in the blanks: The coordination numbers of Ca2+ and F in fluorite are and respectively.

  • A6, 4
  • B4, 2
  • C4, 4
  • D2, 4
  • E4, 6

Q8:

Fill in the blank: Atoms in a body-centered cubic unit cell have a coordination number of .

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